login
A292447
Primes p such that sigma((p + 1) / 2) is a prime q.
3
3, 7, 17, 31, 127, 577, 3361, 4801, 6961, 8191, 31249, 131071, 171697, 524287, 982801, 1062881, 1104097, 1367857, 1407841, 1468897, 2705137, 3770257, 6822817, 7785457, 10941841, 14183137, 15557041, 18495361, 20749681, 25304497, 36278161, 38878561, 44575681
OFFSET
1,1
COMMENTS
A companion sequence of A249902.
Mersenne primes p = 2^k - 1 (A000668) are terms: sigma((p + 1) / 2) = sigma((2^k - 1 + 1) / 2) = sigma((2^(k - 1)) = 2^k - 1.
A subsequence of A178490. - Altug Alkan, Oct 02 2017
LINKS
FORMULA
a(n) = 2*A249902(n) - 1. - Altug Alkan, Oct 02 2017
EXAMPLE
17 is a term because sigma((17 + 1) / 2) = sigma(9) = 13 (prime).
MATHEMATICA
Select[Prime@ Range[10^6], PrimeQ@ DivisorSigma[1, (# + 1)/2] &] (* Michael De Vlieger, Sep 16 2017 *)
PROG
(Magma) [n: n in [1..10^8] | IsPrime(n) and IsPrime(SumOfDivisors((n+1) div 2))]
(PARI) lista(nn) = forprime(p=3, nn, if(isprime(sigma((p+1)/2)), print1(p, ", "))); \\ Altug Alkan, Oct 02 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jaroslav Krizek, Sep 16 2017
STATUS
approved